Some properties of a class of quasi-differentiable functions（the difference of two finite convex functions） are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and c...Some properties of a class of quasi-differentiable functions（the difference of two finite convex functions） are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved.展开更多
This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under m...This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the non- monotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.展开更多
This paper presents a new approach to solve mixed-variable unit commitment(UC) problems with non-smooth cost functions based on a generalized pattern search filter(GPS-filter) algorithm. A GPS-filter algorithm does no...This paper presents a new approach to solve mixed-variable unit commitment(UC) problems with non-smooth cost functions based on a generalized pattern search filter(GPS-filter) algorithm. A GPS-filter algorithm does not require any information about the gradient of the objective function while searching for an optimum solution. At the same time, it is available for solving mixed-variable optimization problems, which is very suitable for UC. A new suitable discrete neighborhood structure with UC characteristics is proposed to improve GPS-filter efficiently. A lot of multiple units' states are fixed before search; hence, the polling search of discrete variable is efficient for a few uncertain units. Numerical experiments are included to demonstrate the proposed approach's ability to handle the highly nonlinear, discontinuous, non-smooth cost functions and mixed variables of the UC problem.展开更多
基金Supported by the State Foundations of Ph.D.Units(20020141013)Supported by the NSF of China(10001007)
文摘Some properties of a class of quasi-differentiable functions（the difference of two finite convex functions） are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved.
基金This research is partly supported by National Outstanding Young Investigator Grant(70225005) of National Natural Science Foundation of China and the Project(70471088) of National Natural Science Foundation of China.
文摘This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the non- monotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.
基金Project Supported by National Natural Science Foundation of China(51277034,51377027)
文摘This paper presents a new approach to solve mixed-variable unit commitment(UC) problems with non-smooth cost functions based on a generalized pattern search filter(GPS-filter) algorithm. A GPS-filter algorithm does not require any information about the gradient of the objective function while searching for an optimum solution. At the same time, it is available for solving mixed-variable optimization problems, which is very suitable for UC. A new suitable discrete neighborhood structure with UC characteristics is proposed to improve GPS-filter efficiently. A lot of multiple units' states are fixed before search; hence, the polling search of discrete variable is efficient for a few uncertain units. Numerical experiments are included to demonstrate the proposed approach's ability to handle the highly nonlinear, discontinuous, non-smooth cost functions and mixed variables of the UC problem.
